Chapter 11 Modern Atomic Theory

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1 Chapter 11 Modern Atomic Theory

2 Rutherford s Atom The concept of a nuclear atom (charged electrons moving around the nucleus) resulted from Ernest Rutherford s experiments. Question left unanswered: how are electrons arranged and how do they move?

3 Rutherford s Atom (cont.)

4 Electromagnetic Radiation

5 Electromagnetic Radiation (cont.) Electromagnetic radiation is given off by atoms when they have been excited by any form of energy, as shown in flame tests.

6 Electromagnetic Radiation (cont.)

7 Figure 11.2: A seagull floating on the ocean moves up and down as waves pass.

8 Electromagnetic Waves Velocity = c = speed of light x 10 8 m/s All types of light energy travel at the same speed. Amplitude = A = measure of the intensity of the wave, i.e. brightness

9 Figure 11.3: The wavelength of a wave is the distance between peaks.

10 Properties of Waves Wavelength (λ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. 7.1

11 Electromagnetic Waves (cont.) Wavelength = λ = distance between two consecutive peaks or troughs in a wave Generally measured in nanometers (1 nm = 10-9 m) Same distance for troughs Frequency = ν = the number of waves that pass a point in space in one second Generally measured in Hertz (Hz), 1 Hz = 1 wave/sec = 1 sec -1 c = λ x ν

12 The back and front of a bridgerigar parrot. University of Glasgow

13 The same bridgerigar parrot seen under ultraviolet light. University of Glasgow

14 Types of Electromagnetic Radiation

15 Planck s Revelation Showed that for certain applications light energy could be thought of as particles or photons

16 Planck s Revelation (cont.) The energy of the photon is directly proportional to the frequency of light.

17 Mystery #1, Black Body Problem Solved by Planck in 1900 Energy (light) is emitted or absorbed in discrete units (quantum). E = h x ν Planck s constant (h) h = 6.63 x J s

18 Mystery #2, Photoelectric Effect Solved by Einstein in 1905 hν Light has both: 1. wave nature 2. particle nature KE e - Photon is a particle of light hν = KE + BE KE = hν - BE 7.2

19 Figure 11.7: Certain gases in the earth s atmosphere reflect back some of the infrared (heat) radiation produced by the earth. This keeps the earth warmer than it would be otherwise.

20 When salts containing Li +, Cu 2+, and Na + dissolved in methyl alcohol are set on fire, brilliant colors result: Li +, red; Cu 2+, green; and Na +, yellow. Hmco Photo Files

21 Problems with Rutherford s Nuclear Model of the Atom Electrons are moving charged particles. Moving charged particles give off energy; therefore the atom should constantly be giving off energy. The electrons should crash into the nucleus, and the atom should collapse!!

22 Emission of Energy by Atoms/Atomic Spectra Atoms that have gained extra energy release that energy in the form of light.

23 Atomic Spectra Line spectrum: very specific wavelengths of light that atoms give off or gain Each element has its own line spectrum, which can be used to identify that element.

24 Atomic Spectra (cont.)

25 Atomic Spectra (cont.)

26 Figure 11.9: A sample of H atoms receives energy from an external source and becomes excited, then releases the energy by emitting photons.

27 Line Emission Spectrum of Hydrogen Atoms

28 An atom can release energy by emitting a photon. A particular color (wavelength) of light carries a particular amount of energy per photon.

29 An atom can release energy by emitting a photon. A particular color (wavelength) of light carries a particular amount of energy per photon.

30 Figure 11.10: When an excited H atom returns to a lower energy level, it emits a photon that contains the energy released by the atom.

31 Figure 11.11: The colors and wavelengths (in nanometers) of the photons in the visible region that are emitted by excited hydrogen atoms.

32 Figure 11.12: Hydrogen atoms have several excited-state energy levels.

33 Atomic Spectra (cont.) The line spectrum must be related to energy transitions in the atom

34 Figure 11.14: (a) Continuous energy levels. Any energy value is allowed. (b) Discrete (quantized) energy levels. Only certain energy states are allowed.

35

36 Atomic Spectra (cont.) The atom is quantized, i.e. only certain energies are allowed.

37 Bohr s Model of the Atom (1913) 1. e - can only have specific (quantized) energy values 2. light is emitted as e - moves from one energy level to a lower energy level 1 E n = -R H ( ) n 2 n (principal quantum number) = 1,2,3, R H (Rydberg constant) = 2.18 x J

38 Bohr s Model Explained spectrum of hydrogen Energy of atom is related to the distance of electron from the nucleus

39 Figure 11.17: The Bohr model of the hydrogen atom represented the electron as restricted to certain circular orbits around the nucleus.

40 Bohr s Model (cont.) Energy of the atom is quantized Atom can only have certain specific energy states called quantum levels or energy levels. When atom gains energy, electron moves to a higher quantum level When atom loses energy, electron moves to a lower energy level Lines in spectrum correspond to the difference in energy between levels

41 Bohr s Model (cont.) Ground state: minimum energy of an atom Therefore electrons do not crash into the nucleus The ground state of hydrogen corresponds to having its one electron in the n=1 level Excited states: energy levels higher than the ground state

42 Bohr s Model (cont.) Distances between energy levels decrease as the energy increases 1st energy level can hold 2e -1, the 2nd 8e -1, the 3rd 18e -1, etc. Further from nucleus = more space = less repulsion Valence shell: the highest-energy occupied ground state orbit

43 n i = 3 n i = 2 n i = 3 n f = 2 E photon = E = E f - E i 1 E f = -R H ( ) n 2 f 1 E i = -R H ( ) n 2 i 1 1 n 2 E = R H ( ) i n 2 f nn f = f = 11

44 Problems with the Bohr Model Only explains hydrogen atom spectrum (and other 1-electron systems) Neglects interactions between electrons Assumes circular or elliptical orbits for electrons (which is not true)

45 Wave Mechanical Model of the Atom Experiments later showed that electrons could be treated as waves Just as light energy could be treated as particles De Broglie Wave-Particle duality: λ=h/p=h/mv h Planck constant

46 Louis Victor de Broglie The Granger Collection

47 Why is e - energy quantized? De Broglie (1924) reasoned that e - is both particle and wave. 2πr = nλ λ = h mu u = velocity of e- m = mass of e-

48 Wave Mechanical Model of the Atom (cont.) The quantum mechanical model treats electrons as waves and uses wave mathematics to calculate probability densities of finding the electron in a particular region in the atom Schrödinger Wave Equation ĤΨ = EΨ Can only be solved for simple systems, but approximated for others

49 Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (Ψ) describes: 1. energy of e - with a given Ψ 2. probability of finding e - in a volume of space Schrodinger s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

50 Orbitals and Energy Levels Solutions to the wave equation give regions in space of high probability for finding the electron. These are called orbitals. Each principal energy level contains one or more sublevels. Sublevels are made up of orbitals.

51 Figure 11.18: A representation of the photo of the firefly experiment.

52 Figure 11.19: The probability map, or orbital, that describes the hydrogen electron in its lowest possible energy state. The more intense the color of a given dot, the more likely it is that the electron will be found at that point.

53 Schrodinger Wave Equation Ψ = fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4,. distance of e - from the nucleus n=1 n=2 n=3

54 Schrodinger Wave Equation Ψ = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Shape of the volume of space that the e - occupies

55 HF/6-31G* electron intracule densities Critical points of Hartree-Fock/6-31G* electron densities in benzene molecule

56

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